This invention relates to a rotor in the form of a non-circular gear wheel or elliptic gear wheel for use in a pumping device, flow meter or the like and more particularly, to a transmission gear device which comprises at least a pair of such non-circular gear wheels provided in improved intermeshing relationship within the casing of the pumping device incorporating the gear device so that the pumping function of the pumping device can be substantially improved over that of the prior art pumping devices in the casing of which the conventional gear wheels are provided in intermeshing relationship. Furthermore, the present invention relates to a method for producing such non-circular gear wheels.
In a pumping device in which two identical non-circular gear wheels such as elliptic gear wheels having longer and shorter radius portions, respectively, the gear wheels will be referred to merely as "non-circular rotors" mounted in meshing relationship within the casing of the pumping device, when fluid is admitted at the inlet port of the pumping device and caused to flow through the interior of the casing to be discharged at the discharge port of the device, the rotors are caused to rotate in the opposite directions to each other and a very small clearance is defined between the inner surface of the casing the tips of the teeth on the longer radius portions of the rotors and between the adjacent inner surfaces of the casing side walls and the sides of the rotors, respectively, so that the fluid is prevented from flowing back and the meshing tooth faces of the two rotors provide fluid-tight seals on the flowing-in and flowing-out sides of the teeth on the rotors as seen in the rotation direction of the rotors to thereby perfectly the backflow of the fluid. Therefore, it is believed that the non-circular or elliptic rotor-type pumping device has a higher volumetric efficiency as compared with the other types of pumping devices employing conventional circular rotors. However, since the rotors rotate while repeating cycles of acceleration and deceleration, as the rotational speed of the rotors increases, the braking resistance developing due to inertia increases proportionally see, for example, applicant's earlier U.S. Pat. No. 2,897,765, issued Aug. 4, 1959 entitled "Driving Apparatus Comprising Modified Elliptic Gear Wheels." Especially, when the operating fluid employed in the pumping device is liquid, substantial vibration and noise take place in the pumping device due to the pulsation of the liquid. The higher the ratio of the rotation volume of the rotor to the delivery amount of the fluid in the rotor (the ratio will be now referred to as "delivery ratio") is, the higher is the volumetric efficiency of the pumping device. The pumping device employing the elliptic rotors of the type referred to above is characterized by that when the flatness of the rotors increases and the acceleration and deceleration of the rotors are substantially great, a high meshing pressure develops between the meshing teeth on the rotors with the maximum pressure angle approaching a predetermined stationary friction angle. And with respect to non-circular or elliptic pitch circles which make a given rolling contact, if the addendum of the teeth on the longer radius portions of the non-circular rotors is designed high, and in other words, if the longer radius portions of the rotors is to be provided with teeth having a great module, the delivery ratio of the rotor will become high, but the so-called interference which cause undercut develops as the roots of gear teeth resulting in shortening of the service life of the rotors. And when the non-circular or elliptic rotor is so designed that the rotor provides a great tool pressure angle to reduce the meshing pressure load on the meshing tooth faces and eliminate the undercut at the tooth root, a predetermined maximum meshing pressure load on the teeth of the intermediate portion between the longer and shorter radius portions of each of the non-circular rotors exceeds a predetermined critical value, as one or both of the meshing rotors wear away even by a slight degree the rotors will disengage from each other to the extent that they will not be able to rotate. Although the delivery ratio of a non-circular or elliptic pitch circle is in inverse relationship to the ratio of the outer periphery radius of the rotor to the distance between the centers of the rotors, it has now been found that when the teeth on the longer and shorter radius portions along the non-circular pitch circle are designed to be a shape having a greater pressure angle on the pitch circle and the teeth on the intermediate portion between the longer and shorter radius portions is designed to be a shape having a smaller pressure angle, no undercut is developed at the roots of the teeth and a higher delivery ratio can be obtained in the associated rotor to thereby develop a maximum meshing pressure load having a moderate value.
The pitch circle of a non-circular or elliptic gear wheel or rotor is defined as a curve along which the rotor rolls about the center of rotation as its axis without slipping and the curve obtainable by each of the following formulas can be considered as such a curve: that is, the curve obtained when it is assumed that at the polar coordinates, a, b and c are numbers relating to the length. d is a positive number from zero to 1 inclusive, x is an independent variable and n is an optional integer, then the length of radius vector .rho..sub.1 is obtained by the following formula: ##EQU1## and when .mu. is a number determined by the above-defined a, b, c and d, then the directional angle .theta..sub.1 is obtained by the following formula: ##EQU2## and the curve engaging the first curve and obtained when it is assumed that at the polar coordinates, the length of the radius vector .rho..sub.2 is obtained by the following formula: ##EQU3## and the directional angle .theta..sub.2 is obtained by the following formula: ##EQU4##
Since the curves of the formulas (1) through (4) inclusive satisfy the above-mentioned conditions, when a blank is cut along the curves referred to hereinabove by a gear cutter having a predetermined or suitable module to form teeth on the blank, a desired non-circular or elliptic gear wheel can be obtained. The thus obtained two identical gear wheels are mounted in intermeshing relationship as the rotors within the casing of a pumping device, flow meter or the like device and in the device, the flow rate flowing through the device is determined by utilizing a crescent clearance defined between the inner surface of the casing and rotors as the measure. In such a case, assuming that a is a constant in the formulas (1) and (3), when the values of b, c and d are selected as being great, the ratio of the shorter radius portion to the longer radius portion along the pitch circle in each rotor (the ratio will be referred to as "flatness" hereinafter) is great and thus, the delivery ratio of the pumping device employing such rotors is increased. In a pumping device or flow meter, the greater the delivery ratio is, the smaller the ratio of the fluid leakage volume to the volume of the admitted fluid is and in other words, the fluid leakage volume is small to reduce difference between the admitted fluid volume and delivered fluid volume and the frictional resistance between the inner surface of the side walls of the pumping device casing and the side surfaces of the rotors resulting in improvement of preciseness of the metering device such as a pumping device. However, when a gear tooth is to be formed on a blank by cutting along the conventional non-circular or elliptic pitch circle, if the tooth is with provided a tooth shape having a module relatively greater with respect to the selected circle, the non-circular circle described by the tips of the teeth on the longer radius portion of the rotor pitch circle will become great to provide a rotor having a great delivery ratio. However, since the cuvature of the pitch circle on the longer radius portion is great, interfere occurs at the roots of the teeth on the longer radius portion to the extent that an undercut will be formed. And when the tooth cutting edge shape of a gear cutter is designed to have a small tool pressure angle, although the width of the tooth tips along which the above-mentioned non-circular outer periphery circle is described will become wide to thereby provide effects which prevent leakage of fluid through the clearance defined between the tips of the teeth on the longer radial portion of the rotor and the inner surface of the casing, interference occurs at the tooth roots on the longer radius portion of the rotor having the great curvature.